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feat(library/tactic): add eassumption tactic, and remove redundant 'subgoals' from apply tactic

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-07-03 12:59:48 -07:00
parent 079592c446
commit abbd054b51
6 changed files with 156 additions and 60 deletions
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49
library/standard/tactic.lean
View file

@ -17,33 +17,34 @@ inductive tactic : Type :=
-- uses them when converting Lean expressions into actual tactic objects. -- uses them when converting Lean expressions into actual tactic objects.
-- The bultin 'by' construct triggers the process of converting a -- The bultin 'by' construct triggers the process of converting a
-- a term of type 'tactic' into a tactic that sythesizes a term -- a term of type 'tactic' into a tactic that sythesizes a term
definition and_then (t1 t2 : tactic) : tactic := builtin_tactic definition and_then (t1 t2 : tactic) : tactic := builtin_tactic
definition or_else (t1 t2 : tactic) : tactic := builtin_tactic definition or_else (t1 t2 : tactic) : tactic := builtin_tactic
definition append (t1 t2 : tactic) : tactic := builtin_tactic definition append (t1 t2 : tactic) : tactic := builtin_tactic
definition interleave (t1 t2 : tactic) : tactic := builtin_tactic definition interleave (t1 t2 : tactic) : tactic := builtin_tactic
definition par (t1 t2 : tactic) : tactic := builtin_tactic definition par (t1 t2 : tactic) : tactic := builtin_tactic
definition repeat (t : tactic) : tactic := builtin_tactic definition repeat (t : tactic) : tactic := builtin_tactic
definition at_most (t : tactic) (k : num) : tactic := builtin_tactic definition at_most (t : tactic) (k : num) : tactic := builtin_tactic
definition discard (t : tactic) (k : num) : tactic := builtin_tactic definition discard (t : tactic) (k : num) : tactic := builtin_tactic
definition focus_at (t : tactic) (i : num) : tactic := builtin_tactic definition focus_at (t : tactic) (i : num) : tactic := builtin_tactic
definition try_for (t : tactic) (ms : num) : tactic := builtin_tactic definition try_for (t : tactic) (ms : num) : tactic := builtin_tactic
definition now : tactic := builtin_tactic definition now : tactic := builtin_tactic
definition assumption : tactic := builtin_tactic definition assumption : tactic := builtin_tactic
definition state : tactic := builtin_tactic definition eassumption : tactic := builtin_tactic
definition fail : tactic := builtin_tactic definition state : tactic := builtin_tactic
definition id : tactic := builtin_tactic definition fail : tactic := builtin_tactic
definition beta : tactic := builtin_tactic definition id : tactic := builtin_tactic
definition apply {B : Type} (b : B) : tactic := builtin_tactic definition beta : tactic := builtin_tactic
definition unfold {B : Type} (b : B) : tactic := builtin_tactic definition apply {B : Type} (b : B) : tactic := builtin_tactic
definition exact {B : Type} (b : B) : tactic := builtin_tactic definition unfold {B : Type} (b : B) : tactic := builtin_tactic
definition trace (s : string) : tactic := builtin_tactic definition exact {B : Type} (b : B) : tactic := builtin_tactic
definition trace (s : string) : tactic := builtin_tactic
infixl `;`:200 := and_then infixl `;`:200 := and_then
infixl `|`:100 := or_else infixl `|`:100 := or_else
notation `!` t:max := repeat t notation `!` t:max := repeat t
notation `⟦` t `⟧` := apply t notation `⟦` t `⟧` := apply t
definition try (t : tactic) : tactic := t | id definition try (t : tactic) : tactic := t | id
notation `?` t:max := try t notation `?` t:max := try t
definition repeat1 (t : tactic) : tactic := t ; !t definition repeat1 (t : tactic) : tactic := t ; !t
definition focus (t : tactic) : tactic := focus_at t 0 definition focus (t : tactic) : tactic := focus_at t 0
definition determ (t : tactic) : tactic := at_most t 1 definition determ (t : tactic) : tactic := at_most t 1
end end

136
src/library/tactic/apply_tactic.cpp
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@ -13,6 +13,7 @@ Author: Leonardo de Moura
#include "kernel/type_checker.h" #include "kernel/type_checker.h"
#include "library/kernel_bindings.h" #include "library/kernel_bindings.h"
#include "library/unifier.h" #include "library/unifier.h"
#include "library/occurs.h"
#include "library/tactic/apply_tactic.h" #include "library/tactic/apply_tactic.h"
namespace lean { namespace lean {
@ -60,51 +61,114 @@ void collect_simple_meta(expr const & e, buffer<expr> & metas) {
}); });
} }
tactic apply_tactic(expr const & _e) { /**
\brief Given a sequence metas: <tt>(?m_1 ...) (?m_2 ... ) ... (?m_k ...)</tt>,
we say ?m_i is "redundant" if it occurs in the type of some ?m_j.
This procedure removes from metas any redundant element.
*/
static void remove_redundant_metas(buffer<expr> & metas) {
buffer<expr> mvars;
for (expr const & m : metas)
mvars.push_back(get_app_fn(m));
unsigned k = 0;
for (unsigned i = 0; i < metas.size(); i++) {
bool found = false;
for (unsigned j = 0; j < metas.size(); j++) {
if (j != i) {
if (occurs(mvars[i], mlocal_type(mvars[j]))) {
found = true;
break;
}
}
}
if (!found) {
metas[k] = metas[i];
k++;
}
}
metas.shrink(k);
}
proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & _e,
bool add_meta, bool add_subgoals) {
goals const & gs = s.get_goals();
if (empty(gs))
return proof_state_seq();
name_generator ngen = s.get_ngen();
type_checker tc(env, ngen.mk_child());
goal g = head(gs);
goals tail_gs = tail(gs);
expr t = g.get_type();
expr e = _e;
expr e_t = tc.infer(e);
buffer<expr> metas;
collect_simple_meta(e, metas);
if (add_meta) {
unsigned num_t = get_expect_num_args(tc, t);
unsigned num_e_t = get_expect_num_args(tc, e_t);
if (num_t > num_e_t)
return proof_state_seq(); // no hope to unify then
for (unsigned i = 0; i < num_e_t - num_t; i++) {
e_t = tc.whnf(e_t);
expr meta = g.mk_meta(ngen.next(), binding_domain(e_t));
e = mk_app(e, meta);
e_t = instantiate(binding_body(e_t), meta);
metas.push_back(meta);
}
}
list<expr> meta_lst = to_list(metas.begin(), metas.end());
lazy_list<substitution> substs = unify(env, t, e_t, ngen.mk_child(), s.get_subst(), get_noop_unifier_plugin(), ios.get_options());
return map2<proof_state>(substs, [=](substitution const & subst) -> proof_state {
name_generator new_ngen(ngen);
type_checker tc(env, new_ngen.mk_child());
expr new_e = subst.instantiate(e);
expr new_p = g.abstract(new_e);
check_has_no_local(new_p, _e, "apply");
substitution new_subst = subst.assign(g.get_name(), new_p);
goals new_gs = tail_gs;
if (add_subgoals) {
buffer<expr> metas;
for (auto m : meta_lst) {
if (!new_subst.is_assigned(get_app_fn(m)))
metas.push_back(m);
}
remove_redundant_metas(metas);
unsigned i = metas.size();
while (i > 0) {
--i;
new_gs = cons(goal(metas[i], subst.instantiate(tc.infer(metas[i]))), new_gs);
}
}
return proof_state(new_gs, new_subst, new_ngen);
});
}
tactic apply_tactic(expr const & e) {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
return apply_tactic_core(env, ios, s, e, true, true);
});
}
tactic eassumption_tactic() {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) { return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals(); goals const & gs = s.get_goals();
if (empty(gs)) if (empty(gs))
return proof_state_seq(); return proof_state_seq();
name_generator ngen = s.get_ngen(); proof_state_seq r;
type_checker tc(env, ngen.mk_child()); goal g = head(gs);
goal g = head(gs); buffer<expr> hs;
goals tail_gs = tail(gs); get_app_args(g.get_meta(), hs);
expr t = g.get_type(); for (expr const & h : hs) {
expr e = _e; r = append(r, apply_tactic_core(env, ios, s, h, false, false));
expr e_t = tc.infer(e);
unsigned num_t = get_expect_num_args(tc, t);
unsigned num_e_t = get_expect_num_args(tc, e_t);
if (num_t > num_e_t)
return proof_state_seq(); // no hope to unify then
for (unsigned i = 0; i < num_e_t - num_t; i++) {
e_t = tc.whnf(e_t);
expr meta = g.mk_meta(ngen.next(), binding_domain(e_t));
e = mk_app(e, meta);
e_t = instantiate(binding_body(e_t), meta);
} }
lazy_list<substitution> substs = unify(env, t, e_t, ngen.mk_child(), s.get_subst(), get_noop_unifier_plugin(), ios.get_options()); return r;
return map2<proof_state>(substs, [=](substitution const & subst) -> proof_state {
name_generator new_ngen(ngen);
type_checker tc(env, new_ngen.mk_child());
expr new_e = subst.instantiate(e);
expr new_p = g.abstract(new_e);
check_has_no_local(new_p, _e, "apply");
substitution new_subst = subst.assign(g.get_name(), new_p);
buffer<expr> metas;
collect_simple_meta(new_e, metas);
goals new_gs = tail_gs;
unsigned i = metas.size();
while (i > 0) {
--i;
new_gs = cons(goal(metas[i], subst.instantiate(tc.infer(metas[i]))), new_gs);
}
return proof_state(new_gs, new_subst, new_ngen);
});
}); });
} }
int mk_apply_tactic(lua_State * L) { return push_tactic(L, apply_tactic(to_expr(L, 1))); } int mk_apply_tactic(lua_State * L) { return push_tactic(L, apply_tactic(to_expr(L, 1))); }
int mk_eassumption_tactic(lua_State * L) { return push_tactic(L, eassumption_tactic()); }
void open_apply_tactic(lua_State * L) { void open_apply_tactic(lua_State * L) {
SET_GLOBAL_FUN(mk_apply_tactic, "apply_tac"); SET_GLOBAL_FUN(mk_apply_tactic, "apply_tac");
SET_GLOBAL_FUN(mk_eassumption_tactic, "eassumption_tac");
} }
} }

1
src/library/tactic/apply_tactic.h
View file

@ -9,5 +9,6 @@ Author: Leonardo de Moura
#include "library/tactic/tactic.h" #include "library/tactic/tactic.h"
namespace lean { namespace lean {
tactic apply_tactic(expr const & e); tactic apply_tactic(expr const & e);
tactic eassumption_tactic();
void open_apply_tactic(lua_State * L); void open_apply_tactic(lua_State * L);
} }

1
src/library/tactic/expr_to_tactic.cpp
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@ -145,6 +145,7 @@ register_unary_num_tac::register_unary_num_tac(name const & n, std::function<tac
static register_simple_tac reg_id(name(g_tac, "id"), []() { return id_tactic(); }); static register_simple_tac reg_id(name(g_tac, "id"), []() { return id_tactic(); });
static register_simple_tac reg_now(name(g_tac, "now"), []() { return now_tactic(); }); static register_simple_tac reg_now(name(g_tac, "now"), []() { return now_tactic(); });
static register_simple_tac reg_assumption(name(g_tac, "assumption"), []() { return assumption_tactic(); }); static register_simple_tac reg_assumption(name(g_tac, "assumption"), []() { return assumption_tactic(); });
static register_simple_tac reg_eassumption(name(g_tac, "eassumption"), []() { return eassumption_tactic(); });
static register_simple_tac reg_fail(name(g_tac, "fail"), []() { return fail_tactic(); }); static register_simple_tac reg_fail(name(g_tac, "fail"), []() { return fail_tactic(); });
static register_simple_tac reg_beta(name(g_tac, "beta"), []() { return beta_tactic(); }); static register_simple_tac reg_beta(name(g_tac, "beta"), []() { return beta_tactic(); });
static register_bin_tac reg_then(g_and_then_tac_name, [](tactic const & t1, tactic const & t2) { return then(t1, t2); }); static register_bin_tac reg_then(g_and_then_tac_name, [](tactic const & t1, tactic const & t2) { return then(t1, t2); });

12
tests/lean/run/tactic20.lean Normal file
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@ -0,0 +1,12 @@
import standard
using tactic
definition assump := eassumption
theorem tst {A : Type} {a b c : A} (H1 : a = b) (H2 : b = c) : a = c
:= by apply trans; assump; assump

17
tests/lean/run/tactic21.lean Normal file
View file

@ -0,0 +1,17 @@
import standard
using tactic
definition assump := eassumption
theorem tst1 {A : Type} {a b c : A} {p : A → A → Bool} (H1 : p a b) (H2 : p b c) : ∃ x, p a x ∧ p x c
:= by apply exists_intro; apply and_intro; assump; assump
theorem tst2 {A : Type} {a b c d : A} {p : A → A → Bool} (Ha : p a c) (H1 : p a b) (Hb : p b d) (H2 : p b c) : ∃ x, p a x ∧ p x c
:= by apply exists_intro; apply and_intro; assump; assump
(*
print(get_env():find("tst2"):value())
*)